The Unbearable Vagueness of Being

Part of the Argumentation Library book series (ARGA, volume 2)


When I consult the literature on the Sorites paradox, I feel like a tourist in a land whose the natives do not try to make me feel welcome.1 The insight, or tolerance principle, that is the basis for generating the paradox is that there are differences too insignificant to make a difference. A single hair cannot make the difference between being bald and not being bald. If it doesn’t make a difference with a person who has no hair at all, then it won’t with one who has a single hair; and so it won’t with one with two hairs; and so on, yielding the absurdity that there are no cases of non-baldness.


Natural Language Induction Step Borderline Case Actual Discourse Vague Predicate 
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  1. 1.
    I am indebted to Ruth Manor for stimulating my interest in the Sorites and providing me with an opportunity to read an earlier version of this essay at Tel Aviv University. I also am indebted to Arthur Cody and Henry Alexander for their invaluable help with this essay.Google Scholar
  2. 2.
    A mountain is thought to be a vague object because of the difficulty in determining whether a certain patch of land is or is not part of the mountain. “It seems obvious that there is no line which sharply divides the matter composing Everest from the matter outside it,” is the way that Michael Tye (1990) puts it (p. 535). Tye does not try to explain why or when anyone would have an interest in making that determination.Google Scholar
  3. 3.
    Travis (1985) seems to be following Bums when he says that “predicates in general exhibit what I would term occasion-sensitivity” (p. 344).Google Scholar
  4. 4.
    McGhee and McLaughlin (1995) seem to have a version of this kind of experiment in mind when they ask us to imagine that 10,000 exactly similar vats of red dye are arranged in a sequence, and a drop of yellow dye is added to the second, two drops to the third, and so on. Then 10,000 identical white ceramic tiles are lowered into the vats and kept there at the same depth for the same length of time. The tiles are arrayed in a row in the same sequence as the vats, and “visual inspection reveals no difference at all between any tile and its immediate neighbor, yet the first tile is unmistakably red, and the last tile unmistakably orange” (p. 203 ). This extraordinary experiment presents many insurmountable logistical problems-with so many vats and tiles mistakes are inevitable. What interests me more is that it never occurs to McGhee and McLaughlin to wonder about the significance of the fact that little or nothing turns on whether or not a tile is said to be red (or orange).Google Scholar
  5. 5.
    Frege’s (1952) use of the metaphor of boundaries has dominated subsequent discussions of vagueness. “A definition of a concept (of a possible predicate) must be complete; it must unambiguously determine, as regards any object, whether or not it falls under the concept…. We may express this metaphorically as follows: the concept must have a sharp boundary” (p. 159).Google Scholar
  6. 6.
    Williamson’s most developed account is in Vagueness (1995). The epistemic approach also is defended in Cargile (1965, pp. 193–202), Campbell (1974, pp. 175–91), Sorensen (1988, pp. 199–253), and Horwich (1990, pp. 81–7).Google Scholar
  7. 7.
    Wright’s (1975) reasoning about why these predicates must have fuzzy boundaries is based on his belief that predicates such as color words are learned ostensively; hence what we learn has boundaries that are defined by the color discriminations that we are able to make merely by the use of our eyes. Wright is wrong about how we learn color predicates because he is wrong about what we learn, namely, how to apply color predicates (to things).Google Scholar
  8. 8.
    Wright (1995) attacks Williamson’s epistemic position on the grounds that it must remain silent about “the nature of the facts which constitute their reference to the relevant precise properties” (p. 153). It must remain silent because if Williamson knew what made the difference he would have the superior cognitive capacity which it is being supposed that humans lack.Google Scholar
  9. 9.
    If the word in the language of these superior beings applies to heaps of sand only when, say, they have more than 53,498 grains, then how do we know that it is properly translated as ‘heap’ rather than ‘rather sizable pile’ or ‘more than 53,498 grains’? This is a question Smith (1995) asks in her review of Williamson’s Vagueness (p. 183). However, whether ‘Joe (with n hairs) is bald’ is said in the language of the superior beings or in ours, the real problem is not about translation from one language to another, but how we can think that we are talking about a language when we refer to the sequence of applications of a predicate to various subjects. Perhaps Smith also wants to point out this problem because she indicates that her real target is the same as mine, “the understanding of semantics that we inherit from Frege” (p. 186).Google Scholar
  10. 10.
    If not every application of the predicate is bivalent, then the induction step may be neither true or false. This is the insight behind the supervaluation approach in Fine (1975, pp. 265–330). If applications of the predicate have different degrees of truth, then the induction step may be true, but repeated applications of modus ponens may lead from applications with a high degree of truth to ones with much lower degrees of truth. For a version of this degrees of truth solution, see Peacocke ( 1981, pp. 121–41). 11 Burns asks us to imagine that the second person who has one more hair has had a hair transplant that distributes his hairs evenly over the top of scalp. She is relying on the fact that hair count is only one of the factors in determining whether something is a case of baldness.Google Scholar
  11. 12.
    This counterexample, which is like the one devised by McGhee and McLaughlin that was cited in footnote four, is introduced by Sorensen (1994, pp. 483–6) in his review of Burns (1991).Google Scholar
  12. 13.
    Philosophers, like Lewis, whose analyses of the sentences of natural language are context-sensitive, are still operating with the model of an artificial formal system when they offer these analyses. Their approach is fatally compromised because they never really supply enough of the details to make clear that they are thinking of when or how someone would actually say the words which they are analyzing. Instead, they operate from outside of discourse, by supplying the context, situation or modality for a sentence they have devised.Google Scholar

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© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  1. 1.University of OregonEugeneUSA

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